Nuprl Lemma : face-zero-and-one
∀[X:j⊢]. ∀[z:{X ⊢ _:𝕀}]. (((z=0) ∧ (z=1)) = 0(𝔽) ∈ {X ⊢ _:𝔽})
Proof
Definitions occuring in Statement :
face-zero: (i=0),
face-one: (i=1),
face-and: (a ∧ b),
face-0: 0(𝔽),
face-type: 𝔽,
interval-type: 𝕀,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
cubical-term_wf,
face-type_wf,
face-and-com,
face-zero_wf,
face-one_wf,
face-0_wf,
iff_weakening_equal,
face-one-and-zero,
interval-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
applyEquality,
thin,
instantiate,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
because_Cache,
hypothesis,
hypothesisEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
independent_functionElimination,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[z:\{X \mvdash{} \_:\mBbbI{}\}]. (((z=0) \mwedge{} (z=1)) = 0(\mBbbF{}))
Date html generated:
2020_05_20-PM-02_43_24
Last ObjectModification:
2020_04_04-PM-04_57_39
Theory : cubical!type!theory
Home
Index